Recall the formula for the Lerner index: $$\underset{\text{Lerner index}} {\underbrace{\frac{P^{m}-C^{\prime}(Q^{m})}{P^{m}}}}=-\frac{P^{\prime} (Q^{m})Q^{m}}{P^{m}}=\underset{\text{inverse price elasticity}} {-\underbrace{\frac{1}{E^d}}\equiv\frac{1}{\eta}}$$